Re: [Phys-l] cosmology

[John Denker <jsd@av8n.com>]

On 09/09/2007 10:24 AM, Jeffrey Schnick wrote:

> I think of "closed" as meaning that the density of the universe will not
> continue decreasing forever but that at some future time the density
> will stop decreasing and start increasing and continue increasing until
> it is again infinite. 


That describes a universe that is time-limited, i.e. bounded
in time.

It is easy to imagine something (perhaps a universe) that is 
bounded in space but not bounded in time.  If something is
unchanging in time it would be described as a cylinder in
spacetime, with its axis along the time direction.

Under /some/ models, any universe that is bounded in space
will also be bounded in time ... which explains why some 
people get sloppy about the distinction ... but properly 
speaking, these are not the same concept.

As for what "closed" properly means in cosmology, I have
no idea.  I know what it means in mathematics, i.e. closed
sets and open sets
  http://en.wikipedia.org/wiki/Closed_set
The cosmological term may have been based on this, but if
so, it has been abused and mutated to the point where no 
useful resemblance remains.

In my previous note I said "closed" when I should have said
bounded in space.